CN112887248A - Communication method based on time domain artificial noise - Google Patents

Communication method based on time domain artificial noise Download PDF

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CN112887248A
CN112887248A CN202110030405.XA CN202110030405A CN112887248A CN 112887248 A CN112887248 A CN 112887248A CN 202110030405 A CN202110030405 A CN 202110030405A CN 112887248 A CN112887248 A CN 112887248A
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frequency domain
artificial noise
eavesdropper
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CN112887248B (en
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董宇涵
阳帆
李志德
耿祖航
权进国
金爽
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Shenzhen International Graduate School of Tsinghua University
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L27/00—Modulated-carrier systems
    • H04L27/26—Systems using multi-frequency codes
    • H04L27/2601—Multicarrier modulation systems
    • H04L27/2602—Signal structure
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B10/00—Transmission systems employing electromagnetic waves other than radio-waves, e.g. infrared, visible or ultraviolet light, or employing corpuscular radiation, e.g. quantum communication
    • H04B10/11—Arrangements specific to free-space transmission, i.e. transmission through air or vacuum
    • H04B10/114—Indoor or close-range type systems
    • H04B10/1149—Arrangements for indoor wireless networking of information
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04K—SECRET COMMUNICATION; JAMMING OF COMMUNICATION
    • H04K1/00—Secret communication
    • H04K1/02—Secret communication by adding a second signal to make the desired signal unintelligible

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Abstract

The invention discloses a communication method based on time domain artificial noise, which comprises the following steps: initializing artificial noise vectors and carrying out precoding to generate target artificial noise orthogonal to a legal channel; carrying out Hermite symmetry on a frequency domain complex signal of a transmitting signal, then carrying out inverse fast Fourier transform to generate a time domain signal vector, inserting a cyclic prefix into the time domain signal vector, and overlapping target artificial noise to form a final transmitting signal; respectively eliminating cyclic prefixes of time domain signals received by a legal user and an eavesdropper, then performing fast Fourier transform to respectively obtain receiving frequency domain signals of the legal user and the eavesdropper, and then respectively performing Hermite inversion symmetry to respectively obtain frequency domain signals Y of the legal userBAnd an eavesdropper frequency domain signal YE(ii) a Using YBRecovering the frequency domain channel matrix of the legal channelFinal received signals of the legal user; using YEAnd recovering the final received signal of the eavesdropper by the frequency domain channel matrix of the eavesdropping channel.

Description

Communication method based on time domain artificial noise
Technical Field
The invention relates to the technical field of wireless optical communication, in particular to a communication method based on time domain artificial noise.
Background
Wireless Optical Communication (OWC) is a technology for Communication by using Wireless Optical waves, has the advantages of wide spectrum and high speed, is considered as a key technology for future indoor multiple access, and is included in the IEEE 802.15.7 standard. At the same time, however, due to the broadcast nature of optical communications, it is very easy to eavesdrop, especially in public places like conference rooms, libraries, shopping malls, etc., and therefore there is a need to increase security using information security techniques.
Conventional information security techniques have mainly focused on upper-layer protocols for communication, using encryption techniques to prevent eavesdropping. However, the encryption technology itself is based on the assumption that the calculation capability of the eavesdropper is limited, and once the key is leaked or the eavesdropper has the calculation capability of brute force cracking, the security cannot be guaranteed. Accordingly, physical layer security techniques have attracted the attention of students in recent years. Among the many physical layer security technologies in the field of Radio Frequency (RF) communication, there is a technology called Artificial Noise (AN), which has a core idea of constructing Artificial Noise by using orthogonality of channels, thereby only interfering with AN eavesdropper and not affecting a legitimate user. This requires the transmitting end to have more degrees of freedom than the legitimate user, which is usually from multiple antennas in radio frequency communication, and this is not applicable to a Single-antenna system like Single-Input Single-Output (SISO). For this reason, there is a document that proposes to utilize the degree of freedom provided by a Cyclic Prefix (CP) in a SISO Orthogonal Frequency Division Multiplexing (OFDM) system.
As described above, the OWC system is also affected by an eavesdropper. However, the OWC system cannot directly use the physical layer security technology in the RF communication system because unlike the RF communication system which transmits complex signals, the OWC system generally transmits unipolar real signals by using an amplitude Modulation and Direct Detection (IM/DD) method. This requires redesigning the physical layer security techniques of the OWC system. For example, the scholars MostafaA and Lampe L first propose to apply AN to AN OWC system to improve the security performance of the system; then Arfaoui MA, Zaid H, Rezki Z, etc. further explore AN AN-based optimal beamforming scheme in a Multiple-Input Single-Output (MISO) OWC system; furthermore Cho S, Chen G and Coon J P propose a non-orthogonal AN scheme for optimizing OWC system security performance in the case of random distribution of eavesdroppers. However, the above-mentioned secure communication scheme using AN utilizes spatial freedom, requires support of multiple light sources, and is not suitable for SISO single light source system.
Disclosure of Invention
Based on the above, the present invention provides a signal processing method based on time domain artificial noise, which is used for improving the security performance of a wireless Optical communication system of direct current biased Optical OFDM (DC-biased Optical OFDM, DCO-OFDM), and the core idea is to use a cyclic prefix in DCO-OFDM to construct artificial noise orthogonal to a legal channel, so as to improve the security rate of the system.
A communication method based on time domain artificial noise comprises the following steps: constructing artificial noise, constructing a transmitting signal and processing a receiving signal; constructing the artificial noise includes steps S11-S12: s11, initializing an artificial noise vector; s12, pre-coding the initialized artificial noise vector to generate target artificial noise orthogonal to a legal channel; the legal channel is a transmission channel from a transmitting terminal to a legal user; constructing the transmission signal includes steps S21 to S23: s21, carrying out Hermitian symmetry on the frequency domain complex signal of the transmitting signal; s22, performing inverse fast Fourier transform on the frequency domain signal subjected to Hermite symmetry to generate a time domain signal vector; s23, inserting a cyclic prefix into the generated time domain signal vector, and overlapping the target artificial noise to obtain a final transmitting signal; the processing of the received signal includes steps S31 to S33: s31, eliminating the cyclic prefix of the time domain signal received by the legal user and the time domain signal received by the eavesdropper, and then performing fast Fourier transform to correspondingly obtain the receiving frequency domain signal of the legal user and the receiving frequency domain signal of the eavesdropper; s32, respectively making Hermite inversion symmetry on the receiving frequency domain signal of the legal user and the receiving frequency domain signal of the eavesdropper, and correspondingly obtaining the frequency domain signal of the legal user and the frequency domain signal of the eavesdropper; s33, restoring the final received signal of the legal user by using the frequency domain signal of the legal user and the frequency domain channel matrix of the legal channel; and restoring the final received signal of the eavesdropper by using the eavesdropper frequency domain signal and the frequency domain channel matrix of the eavesdropper channel.
The invention has the beneficial effects that: the cyclic prefix in DCO-OFDM is utilized to construct time domain artificial noise orthogonal to a legal channel, and when the artificial noise passes through the legal channel, the artificial noise is mutually offset in the time domain due to multipath effect caused by reflection, so that the influence on a legal user is eliminated, only an eavesdropper is interfered, and the confidentiality of a communication system is improved. Meanwhile, the covariance matrix of the artificial noise is optimized according to the expression of the confidentiality rate, and the confidentiality performance of the system is further improved through the mode.
Drawings
FIG. 1 is a flow chart of the artifact assisted DCO-OFDM of the present invention;
FIG. 2 is a diagram of the secret rate R of the present inventionsA graph of the variation of the SNR with respect to the signal-to-noise ratio;
FIG. 3 is a diagram of the secret rate R of the present inventionsAnd (3) a change relation diagram of the artificial noise power ratio alpha.
Detailed Description
The invention is further described with reference to the following figures and detailed description of embodiments.
The embodiment of the invention provides a communication method based on time domain artificial noise, namely, the artificial noise is superposed on information to be transmitted in an optical signal transmitted by a transmitting terminal, and the artificial noise is used for improving the confidentiality of a DCO-OFDM wireless optical communication system. The core idea is that cyclic prefix in DCO-OFDM is utilized to construct artificial noise orthogonal to a legal channel, and when the artificial noise passes through the legal channel, the artificial noise is mutually offset in a time domain due to multipath effect caused by reflection, so that the artificial noise does not exist in a received signal of a legal user, the influence on the legal user is eliminated, and only interference is caused to an eavesdropper.
The embodiment of the invention considers a DCO-OFDM wireless optical communication system of three users. The transmitting end includes a single user named Alice, which transmits an optical signal using a single Light source, such as a Light Emitting Diode (LED) or a Laser Diode (LD). The receiving end includes a legitimate user named Bob and an eavesdropper named Eve, which receive the optical signal with a single photodetector such as a Photodiode (PD), respectively. The system flow is shown in fig. 1, and it should be noted that S/P in fig. 1 represents serial-to-parallel conversion, and P/S represents parallel-to-serial conversion.
The number of DCO-OFDM subcarriers is represented as 2N, and the length of the cyclic prefix is represented as NcpIn which N iscpDepending on the delay spread of the actual channel, 1/8 is typically taken for the number of OFDM subcarriers 2N. The insertion and elimination of cyclic prefix can be expressed by matrix transformation, and the insertion matrix and the elimination matrix are respectively
Figure BDA0002891898960000031
And
Figure BDA0002891898960000032
wherein the content of the first and second substances,
Figure BDA0002891898960000033
representing an identity matrix I of 2 Nx 2N2NLast NcpA matrix of rows, the superscript T representing the transpose of the matrix,
Figure BDA0002891898960000034
the expression size is 2 NXNcpThe zero matrix of (2). For the receiving end, due to the multipath effect caused by the reflection of the light wave, the PD of the receiving end receives multiple paths of light signals, and the impulse responses of the first path of signals received by the legal user Bob and the eavesdropper Eve are respectively defined as hB(l) And hE(l) Where L is 0,1, …, L, and L denotes the maximum delay. h isB(l) And hE(l) The Line-of-Sight (LOS) component is indicated when l is 0, and the Non-Line-of-Sight (NLOS) component is indicated when l > 0.
The communication method based on the time domain artificial noise provided by the embodiment of the invention comprises the steps of constructing the artificial noise, constructing a transmitting signal and processing a receiving signal; wherein, constructing the artificial noise comprises steps S11-S12: s11, initializing an artificial noise vector z; s12, pre-coding the initialized artificial noise vector z to generate a target artificial noise a orthogonal to a legal channel; wherein, the legal channel is a transmission channel between a transmitting terminal and a legal user. Constructing the transmission signal includes steps S21 to S23: s21, carrying out Hermitian symmetry on the frequency domain complex signal S of the transmitting signal; s22, and converting the frequency domain signal S after Hermite symmetrySPerforming inverse fast Fourier transform to generate a time domain signal vector s; s23, inserting cyclic prefix into the generated time domain signal vector S, and superposing the target artificial noise to obtain a final emission signal xA. The processing of the received signal includes steps S31 to S33: s31, eliminating the cyclic prefix of the time domain signal received by the legal user and the time domain signal received by the eavesdropper, and then performing Fourier transform to correspondingly obtain the received frequency domain signal of the legal user
Figure BDA0002891898960000041
And the received frequency domain signal of the eavesdropper
Figure BDA0002891898960000042
S32, receiving frequency domain signals of legal users respectively
Figure BDA0002891898960000043
And the received frequency domain signal of the eavesdropper
Figure BDA0002891898960000044
Making Hermite inverse symmetry to correspondingly obtain legal user frequency domain signal YBAnd an eavesdropper frequency domain signal YE(ii) a S33, utilizing legal user frequency domain signal YBAnd frequency domain channel matrix of legal channel
Figure BDA0002891898960000045
Recovery of the final received signal of a legitimate user
Figure BDA0002891898960000046
Using the eavesdropper frequency domain signal YEAnd eavesdropping the frequency domain channel matrix of the channel
Figure BDA0002891898960000047
Recovering the final received signal of the eavesdropper
Figure BDA0002891898960000048
The method comprises the following specific steps:
s11, the initial artificial noise can be expressed as a length NcpVector of (2)
Figure BDA0002891898960000049
Wherein
Figure BDA00028918989600000410
For the real number domain, z follows a zero mean Gaussian distribution, and the covariance matrix is ∑z＝E{zzTDenotes mathematical expectation, zTRepresenting the transpose of z.
S12, constructing a precoding matrix to precode the initialized artificial noise vector z, wherein the precoding matrix is
Figure BDA00028918989600000411
And the column vector of G is located at RcpHBIn the null space of (a), i.e.:
RcpHBG＝0 (1)
wherein the content of the first and second substances,
Figure BDA00028918989600000412
the time domain channel matrix representing the time domain channel from the transmitting end to the legal user is a normal diagonal matrix, which can be written as:
Figure BDA0002891898960000051
similarly, h isB(l) Is replaced by hE(l) A time domain channel matrix H between the transmitting end and the eavesdropper can be obtainedE. Due to HBIs a lower triangular matrix and the diagonal element is greater than 0, so HBIs a reversible matrix, whereby the precoding matrix is
Figure BDA0002891898960000052
Wherein
Figure BDA0002891898960000053
Represents HBThe inverse of (a) is,
Figure BDA0002891898960000054
is expressed as size Ncp×NcpThe identity matrix of (2).
And precoding the initialized artificial noise vector z by using a precoding matrix, namely:
a＝Gz (4)
wherein a is the vector representation of the target artificial noise obtained by pre-coding, and
Figure BDA0002891898960000055
each element in vector a represents an artificial noise symbol transmitted in each slot in one OFDM period. The target artificial noise a generated by pre-coding is orthogonal to the legal channel, so that it does not appear in the received signal of the legal user.
S21, since the transmitted time domain signal is real, hermitian symmetry is required for the complex signal in the frequency domain. Each OFDM block thus carries only (N-1) frequency domain symbols, with one complex vector S ═ S1,S2,…,SN-1]TRepresenting a frequency domain complex signal. The frequency domain signal obtained after Hermite symmetry is expressed as
Figure BDA0002891898960000056
Wherein
Figure BDA0002891898960000057
Wherein [ ·]*Representing conjugation.
S22, and then SSGenerating a time-domain signal vector s ═ F through Inverse Fast Fourier Transform (IFFT)HSS＝[s1,s2,…,s2N-1]TWherein F and FHFast Fourier Transform (FFT) matrix and IFFT matrix are shown, respectively. The nth element of s can be represented as
Figure BDA0002891898960000061
Where Φ { · } represents the real part of the complex number, e is a natural constant. Will matrix 2FHThe middle 2 nd column to the Nth column form a submatrix defined as
Figure BDA0002891898960000062
Then s can also be expressed as
Figure BDA0002891898960000063
After the time-domain signal S is generated S23, a cyclic prefix needs to be inserted to combat inter-symbol interference. The insertion of the cyclic prefix can be expressed in the form of a matrix transformation using a matrix of Tcp. Finally, adding the constructed target artificial noise a to form a final transmitting signal xAIs shown as
Figure BDA0002891898960000064
Considering the total power limit of the transmitted signal as P, the power allocated to the information part and the artificial noise part is PsAnd Pa. By alpha epsilon [0,1]Indicates assignment to PaIn a ratio of (i.e. P)a＝αP，Ps＝(1-α)PFor power PsAnd PaThe following constraints are satisfied:
Figure BDA0002891898960000065
Figure BDA0002891898960000066
where | · | | represents the euclidean norm and E {. denotes the mathematical expectation.
S31, after the legal user Bob receives the time domain signal, firstly eliminating the cyclic prefix, then carrying out fast Fourier transform, wherein the elimination of the cyclic prefix adopts a matrix RcpMatrix transformation is carried out, and after fast Fourier transformation, the receiving frequency domain signal of a legal user is obtained
Figure BDA0002891898960000067
Is composed of
Figure BDA0002891898960000068
Similarly, the receiving frequency domain signal of the eavesdropper is obtained
Figure BDA0002891898960000069
Is composed of
Figure BDA00028918989600000610
Wherein the content of the first and second substances,
Figure BDA0002891898960000071
Figure BDA0002891898960000072
and
Figure BDA0002891898960000073
respectively indicating the reception of a legal user and an eavesdropper in the ith time slotTo a frequency domain signal.
Figure BDA0002891898960000074
And
Figure BDA0002891898960000075
respectively representing Additive White Gaussian Noise (AWGN) received by Bob and Eve, and the noise power is sigma2，
Figure BDA0002891898960000076
The expression size is (N)cp+2N)×(Ncp+2N) identity matrix.
Order to
Figure BDA0002891898960000077
Equivalent to FRcpHBTcpFHAnd order
Figure BDA0002891898960000078
Equivalent to FRcpHETcpFHThen, then
Figure BDA0002891898960000079
And
Figure BDA00028918989600000710
can be written in the form of a diagonal matrix, i.e.
Figure BDA00028918989600000711
Figure BDA00028918989600000712
Wherein HB,iAnd HE,iRespectively representing the frequency responses of the ith subcarrier from the transmitting end Alice to the legitimate user Bob and the eavesdropper Eve.
S32, receiving frequency domain signal to legal user
Figure BDA00028918989600000713
Making Hermite inverse symmetry to obtain legal user frequency domain signal YB＝[YB,1,...,YB,N-1]T(ii) a Receiving frequency domain signal for eavesdropper
Figure BDA00028918989600000714
Making Hermite inverse symmetry to obtain eavesdropper frequency domain signal YE＝[YE,1,...,YE,N-1]TWherein:
Figure BDA00028918989600000715
Figure BDA00028918989600000716
s33, the frequency domain channel matrices of the legitimate user and the eavesdropper can be defined as:
Figure BDA00028918989600000717
Figure BDA00028918989600000718
wherein the content of the first and second substances,
Figure BDA00028918989600000719
the definition given above is that of the matrix 2FHA submatrix formed by the 2 nd column to the Nth column; while
Figure BDA00028918989600000720
Is that
Figure BDA00028918989600000721
Is transposed, therefore
Figure BDA00028918989600000722
Can be composed of
Figure BDA00028918989600000723
And (6) obtaining.
Thus, YBAnd YECan be rewritten as:
Figure BDA00028918989600000724
Figure BDA00028918989600000725
finally, the signals recovered at the legal user receiving end and the eavesdropper receiving end are respectively:
Figure BDA0002891898960000081
Figure BDA0002891898960000082
in addition, in the case where the power allocated to the information part and the artificial noise part satisfies a preset constraint condition, the covariance matrix Σ is adjustedzTo maximize the privacy rate of the communication system. Secret rate RsExpressed as:
Rs＝[Θ(S；YB)-Θ(S；YE)]+ (20)
wherein [ theta (S; Y)B)-Θ(S；YE)]+Representing 0 and [ theta (S; Y)B)-Θ(S；YE)]The largest of (A), Θ (S; Y)B) Frequency domain complex signal S representing transmission signal and legal user frequency domain signal YBMutual information between theta (S; Y)E) Frequency domain complex signal S representing transmission signal and eavesdropper frequency domain signal YEThe mutual information between them.
The goal of artificial noise optimization is to satisfy the power constraint (9) by adjusting sigmazMaximizing the privacy rate. The optimization problem is expressed as follows:
Figure BDA0002891898960000083
wherein
Figure BDA0002891898960000084
Representing a covariance matrix ∑zSemi-positive nature of (2), constraint of E { | | a | | non-phosphor cells in (9)2}＝Tr{GΣzGTAnd (4) represents the trace of the matrix.
Covariance matrix sigma of complex signal S in frequency domainS＝E{SSTAt fixed, the mutual information in equation (20) depends on the probability distribution of S. Using signal processing techniques such as probability shaping, the mutual information can be maximized, and in particular, can be represented as
Figure BDA0002891898960000085
Figure BDA0002891898960000086
Wherein K is equivalent to
Figure BDA0002891898960000087
IN-1An identity matrix of size (N-1) × (N-1) is represented. It can be seen that the expression in equation (22) is equal to ∑zIndependently, for equation (23), it can be approximated as:
Figure BDA0002891898960000091
it can be seen that the final expression of equation (24) has only the last term log2det(KΣzKH+4σ2IN-1) And sigmazIn this regard, optimization problem equation (21) may then be rewritten as:
Figure BDA0002891898960000092
this is a convex optimization problem that can be solved using algorithms such as gradient descent or interior point methods to maximize the privacy rate.
The effect of the present invention is verified by a specific example.
Consider a SISO DCO-OFDM OWC system comprising a single light source sender Alice, a single photodetector legitimate user Bob and a single photodetector eavesdropper Eve. OFDM comprises 64 subcarriers with 2N, length N of cyclic prefixcp8. Suppose AWGN has a power of σ2The Signal-to-Noise Ratio (SNR) can be expressed as SNR of 10log 110And P. The elements of the frequency domain complex signal S are assumed to be independent and uniformly distributed random variables, and the variance is betasI.e. covariance matrix of ∑S＝E{SST}＝βsIN-1，IN-1Is an identity matrix of (N-1) × (N-1). Wherein, betasSatisfies the power constraint (8), i.e. betasIs equivalent to
Figure BDA0002891898960000093
In addition, for the channel part, it is assumed that the line-of-sight channel gain is hB(0)＝hE(0) 1. The non-line-of-sight channels have 6 channels and the gains are respectively hB(l)＝γθB,lAnd hE(l)＝γθE,lWhere l ═ 1.. 6. { θ }B,lAnd { theta }E,lAnd the independent and uniformly distributed random variables are uniformly distributed between 0 and 1, and the gamma is 0.3 to represent the attenuation coefficient of the reflection. FIG. 2 shows the secret rate RsRegarding the variation relationship of the SNR, the target artificial noise power ratio to be added is, in order, 0,0.1,0.2, 0.5. FIG. 3 shows RsRegarding the α variation relationship, the SNR is 10,20,30dB in order. Each RsChannel simulations were performed 100 times and then averaged. It can be seen that compared with the case of not adding artificial noise, i.e. α is 0, the security performance of the system can be significantly improved after adding artificial noise, and the security performance can be improved along with the improvement of α. However, when α reaches a threshold value, increasing α will causeThe power of the signal portion becomes less and less, which in turn impairs the security performance. As can be seen from fig. 3, the privacy performance is optimized when α ≈ 0.7 under the current channel conditions. In the case of a general channel, a is 0.5, which can achieve better security performance.
The foregoing is a more detailed description of the invention in connection with specific preferred embodiments and it is not intended that the invention be limited to these specific details. For those skilled in the art to which the invention pertains, several equivalent substitutions or obvious modifications can be made without departing from the spirit of the invention, and all the properties or uses are considered to be within the scope of the invention.

Claims (9)

1. A communication method based on time domain artificial noise is characterized by comprising the following steps: constructing artificial noise, constructing a transmitting signal and processing a receiving signal;
constructing the artificial noise includes steps S11-S12:
s11, initializing an artificial noise vector;
s12, pre-coding the initialized artificial noise vector to generate target artificial noise orthogonal to a legal channel; the legal channel is a transmission channel from a transmitting terminal to a legal user;
constructing the transmission signal includes steps S21 to S23:
s21, carrying out Hermitian symmetry on the frequency domain complex signal of the transmitting signal;
s22, performing inverse fast Fourier transform on the frequency domain signal subjected to Hermite symmetry to generate a time domain signal vector;
s23, inserting a cyclic prefix into the generated time domain signal vector, and overlapping the target artificial noise to obtain a final transmitting signal;
the processing of the received signal includes steps S31 to S33:
s31, eliminating the cyclic prefix of the time domain signal received by the legal user and the time domain signal received by the eavesdropper, and then performing fast Fourier transform to correspondingly obtain the receiving frequency domain signal of the legal user and the receiving frequency domain signal of the eavesdropper;
s32, respectively making Hermite inversion symmetry on the receiving frequency domain signal of the legal user and the receiving frequency domain signal of the eavesdropper, and correspondingly obtaining the frequency domain signal of the legal user and the frequency domain signal of the eavesdropper;
s33, restoring the final received signal of the legal user by using the frequency domain signal of the legal user and the frequency domain channel matrix of the legal channel; and restoring the final received signal of the eavesdropper by using the eavesdropper frequency domain signal and the frequency domain channel matrix of the eavesdropper channel.
2. The time-domain artificial noise-based communication method according to claim 1, wherein the insertion and removal of the cyclic prefix are implemented in the form of matrix transformation, and the insertion matrix and the removal matrix are respectively
Figure FDA0002891898950000011
And
Figure FDA0002891898950000012
wherein the content of the first and second substances,
Figure FDA0002891898950000013
representing an identity matrix I of 2 Nx 2N2NLast NcpA matrix of rows, the superscript T representing the transpose of the matrix,
Figure FDA0002891898950000014
the expression size is 2 NXNcpZero matrix of, NcpAnd 2N is the OFDM subcarrier number of the communication system for the length of the cyclic prefix.
3. The time-domain artifact-based communication method as claimed in claim 2, wherein the artifact vector is initialized to a length N in step S11cpA vector z of
Figure FDA0002891898950000015
Wherein
Figure FDA0002891898950000016
For the real number domain, z follows a zero mean Gaussian distribution, and the covariance matrix is ∑z＝E{zzTDenotes mathematical expectation, zTRepresenting the transpose of z.
4. The time-domain artificial noise based communication method according to claim 3, wherein the precoding matrix for precoding the initialized artificial noise vector in step S12 is
Figure FDA0002891898950000021
And the column vector of G is located at RcpHBIn the null space of (1), i.e. RcpHBG＝0，
Figure FDA0002891898950000022
The time domain channel matrix from the transmitting terminal to the legal user is a normal diagonal matrix; thus, the precoding matrix
Figure FDA0002891898950000023
Wherein
Figure FDA0002891898950000024
Represents HBThe inverse of (1);
the generated target artificial noise a is Gz, and
Figure FDA0002891898950000025
each element in vector a represents an artificial noise symbol transmitted in each slot in one OFDM period.
5. A time-domain artificial noise based communication method according to claim 3, wherein the power allocated to the information part and the artificial noise part satisfies a preset constraint condition under a total power limit of the final transmitted signal.
6. The time-domain artificial noise based communication method according to claim 5, wherein the preset constraint condition is:
in the case where the total power limit of the final transmission signal is P, the power allocated to the information part and the artificial noise part is PsAnd PaUsing α ∈ [0,1 ]]Indicates assignment to PaIn a ratio of (i.e. P)a＝αP，PsFor power P, (1- α) PsAnd PaThe following constraints are satisfied:
Figure FDA0002891898950000026
Figure FDA0002891898950000027
where E {. denotes a mathematical expectation, vector a denotes the target artificial noise, and vector s denotes the time-domain signal vector.
7. The time-domain artifact-based communication method as claimed in claim 2, wherein said final transmitted signal formed in step S23 is xA＝Tcps + a, vector s representing the time-domain signal vector, and vector a representing the target artifact.
8. The time-domain artifact-based communication method as claimed in claim 1, wherein in step S33:
restoring the final received signal of the legal user by using the frequency domain signal of the legal user and the frequency domain channel matrix of the legal channel, wherein the restoring comprises the following steps:
Figure FDA0002891898950000031
wherein
Figure FDA0002891898950000032
I.e. the final received signal of the legitimate user,
Figure FDA0002891898950000033
frequency domain channel matrix for legal channel
Figure FDA0002891898950000038
Inverse of (A), (B), (C), (BThe legal user frequency domain signal;
restoring the final received signal of the eavesdropper by using the frequency domain signal of the eavesdropper and the frequency domain channel matrix of the eavesdropper channel, wherein the method comprises the following steps:
Figure FDA0002891898950000034
wherein
Figure FDA0002891898950000035
I.e. the final received signal of the eavesdropper,
Figure FDA0002891898950000036
frequency domain channel matrix for eavesdropping on channel
Figure FDA0002891898950000037
Inverse of (A), (B), (C), (EIs the eavesdropper frequency domain signal.
9. The time-domain artifact-based communication method as recited in claim 5, further comprising: in the case where the power allocated to the information part and the artificial noise part satisfies a preset constraint condition, by adjusting the covariance matrix ΣzTo maximize the privacy rate of the communication system.
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